Step 1 :
Divide $ 925127 $ by $ 856641 $ and get the remainder

$$ 925127 : 856641 = 1 \text{ ( remainder is } \color{blue}{ 68486 } \text{ ) } $$

The remainder is positive ($ 68486 > 0 $), so we will continue with division.

Step 2 :
Divide $ 856641 $ by $ \color{blue}{ 68486 } $ and get the remainder

$$ 856641 : 68486 = 12 \text{ ( remainder is } \color{blue}{ 34809 } \text{ ) } $$

The remainder is still positive ($ 34809 > 0 $), so we will continue with division.

Step 3 :
Divide $ 68486 $ by $ \color{blue}{ 34809 } $ and get the remainder

$$ 68486 : 34809 = 1 \text{ ( remainder is } \color{blue}{ 33677 } \text{ ) } $$

The remainder is still positive ($ 33677 > 0 $), so we will continue with division.

Step 4 :
Divide $ 34809 $ by $ \color{blue}{ 33677 } $ and get the remainder

$$ 34809 : 33677 = 1 \text{ ( remainder is } \color{blue}{ 1132 } \text{ ) } $$

The remainder is still positive ($ 1132 > 0 $), so we will continue with division.

Step 5 :
Divide $ 33677 $ by $ \color{blue}{ 1132 } $ and get the remainder

$$ 33677 : 1132 = 29 \text{ ( remainder is } \color{blue}{ 849 } \text{ ) } $$

The remainder is still positive ($ 849 > 0 $), so we will continue with division.

Step 6 :
Divide $ 1132 $ by $ \color{blue}{ 849 } $ and get the remainder

$$ 1132 : 849 = 1 \text{ ( remainder is } \color{blue}{ 283 } \text{ ) } $$

The remainder is still positive ($ 283 > 0 $), so we will continue with division.

Step 7 :
Divide $ 849 $ by $ \color{blue}{ 283 } $ and get the remainder

$$ 849 : \color{blue}{ \boxed { 283 }} = 3 \text{ ( remainder is } \color{blue}{ 0 } \text{ ) } $$

The remainder is zero => GCD is the last divisor $ \color{blue}{ \boxed { 283 }} $.

This solution can be visualized using a Venn diagram.

The GCD equals the product of the numbers at the intersection.

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